"Exxon engaged in egregious, intentional fraud by which it sought to deprive Alabama of hundreds of millions of dollars, probably well over $1bn," an Alabama Circuit Court judge wrote in an order signed on Thursday.
"Exxon has shown no contrition or even changed its royalty payment calculation. Only a substantial punitive award can punish Exxon and deter it and others," the judge added.
Exxon Mobil plans to appeal to the state's Supreme Court, which attorneys estimated could take up to one and a half years to rule.
Fraud case
In December a jury decided that Exxon Mobil had fraudulently underpaid the state royalties for natural gas wells drilled of the coast of Alabama.
While the jury awarded the state $87.7m in damages, they also imposed punitive damages of $3.42bn.
In April, Exxon Mobil's lawyers argued the punitive damages were excessive, more than 30 times the highest amount the Alabama Supreme Court had ever awarded in a fraud case.
The state's lawyers argued that a record verdict was needed to send out a warning to the giant oil company.
In the ruling on Thursday, the judge agreed with the state's attorneys.
Alabama filed the suit against Exxon in 1999, before the company merged with Mobil.
Exxon results
In April, Exxon Mobil's profits surge to $5.05bn (£3.5bn) during the first three months of the year.
This compared to $3.35bn for the first quarter of 2000, itself a sharp rise over the previous year.
Exxon Mobil, which trades as Esso and Mobil in Europe, attributed the strong results to high oil and natural gas prices, and better profits on fuels, including petrol.
First quarter income rose to $57.28bn compared to $54.1bn a year ago.